Limit Cycles of Differential Equations
2nd Edition
Published on 22. January 2024
IX, 238 pages
978-3-030-59656-9 (ISBN)
Description
This textbook contains the lecture series originally delivered at the "Advanced Course on Limit Cycles of Differential Equations" in the Centre de Recerca Matemàtica Barcelona in 2006.
The topics covered are the center-focus problem for polynomial vector fields, and the application of Abelian integrals to limit cycle bifurcations. Both topics are related to Hilbert's sixteenth problem. In particular, the book will be of interest to students and researchers working in the qualitative theory of dynamical systems.This second edition provides updates, further clarifications and remarks, and includes an expanded list of references.
More details
Series
Edition
2nd ed. 2024
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Target group
Professional and scholarly
Illustrations
IX, 238 p. 21 illus., 5 illus. in color.
File size
2,89 MB
ISBN-13
978-3-030-59656-9 (9783030596569)
DOI
10.1007/978-3-030-59656-9
Schweitzer Classification
Other editions
Additional editions
Colin Christopher | Chengzhi Li | Joan Torregrosa
Limit Cycles of Differential Equations
Book
01/2024
2nd Edition
Birkhäuser
€29.95
Shipment within 7-9 days
Persons
Colin Christopher
is Associate Head of School at the University of Plymouth in Devon, UK.
Chengzhi Li is Professor Emeritus at the Peking University in China.
Joan Torregrosa is Associate Professor at the Universitat Autònoma de Barcelona in Bellaterra, Spain.
Content
Part I: Around the Center-Focus Problem.- 1 Centers and Limit Cycles.- 2 Darboux Integrability.- 3 Liouvillian Integrability.- 4 Symmetry.- 5 Cherkas' Systems.- 6 Monodromy.- 7 The Tangential Center-Focus Problem.- 8 Monodromy of Hyperelliptic Abelian Integrals.- 9 Holonomy and the Lotka-Volterra System.- 10 Other Approaches.- Part II: Abelian Integrals and Applications to the Weak Hilbert's 16th Problem.- 1 Hilbert's 16th Problem and Its Weak Form.- 2 Abelian Integrals and Limit Cycles.- 3 Estimate of the Number of Zeros of Abelian Integrals.- 4 A Unified Proof of the Weak Hilbert's 16th Problem for n=2.
